# Enthalpy Change - Formula, Standard Enthalpy of Formation, Reaction, Relation between Enthalpy, Entropy and Gibbs Free Energy

## What is Enthalpy?

Enthalpy is a term derived from a Greek word that means ‘heat inside’; it is the total amount of energy present in a thermodynamic system capable of doing mechanical work. The value of enthalpy is completely dependent on the parameters of temperature, the composition of the system, and pressure. In terms of formula, enthalpy can be defined as the sum of internal energy and the multiplication product of pressure and volume components of a system. The unit of enthalpy is the same as energy, Joules.

H= E + PV

H= Enthalpy

E= Internal Energy (Internal Energy is sometimes denoted by ‘U’)

P= Pressure, V= Volume

## The First Law of Thermodynamics

As per the first law of thermodynamics, also known as the law of conservation of energy: ‘Energy can neither be created nor destroyed; it can only be transferred from one form to another. Therefore, the amount of energy transferred between the systems is equal to the amount of change in the internal energy of a particular system.

The energy that is added to a matter to bring about a change in the phase, is enthalpy. Based on the phase transition that the energy promotes, enthalpy is further named as enthalpy of vaporization, enthalpy of fusion and more.

- Enthalpy of Vaporization (latent heat) = Energy involved in changing the state of matter from liquid to gaseous.
- Enthalpy of Fusion= Energy absorbed by a solid when it melts into a liquid.

It is crucial to note that there are no direct methods available to estimate the enthalpy of a system. So, the only way to understand the energy transfer process is to calculate the change in the system's enthalpy.

## Enthalpy Change

Enthalpy is a state function, so it entirely depends on the initial and final state of the reaction and is independent of the path undertaken to reach the state. The standard enthalpy of a reaction or enthalpy change is the difference in the sum of enthalpies of the products and the sum of enthalpies of reactants. The change in enthalpy for a chemical reaction is denoted by Δt H.

## a. Standard Enthalpy of Formation:

The standard enthalpy of formation is the amount of enthalpy change involved in the formation of one mole of any compound from its standard state elements. Example: The standard enthalpy of formation for 1 mole of water.

H2 + ½ O2 --🡪 H2O   Δf H˚ = -286kJ

## b. Standard Enthalpy of Reaction:

The amount of energy involved in transforming one mole of matter under standard operating conditions is called the standard enthalpy of reaction. In reality, the standard enthalpy of reaction is the change in the enthalpy of a reaction calculated by estimating the difference in the standard enthalpy of formation of products and standard enthalpy of formation of reactants. Enthalpy is an additive property, so the standard enthalpies of formation can be added.

Example: For calculating the standard enthalpy of reaction of the combustion of methane.

CH4 + 2O2 ---🡪 CO2 + 2H2O

The following steps need to be followed:

1. Summation of standard enthalpy of formation of methane and oxygen.
2. Summation of standard enthalpy of formation of water and carbon dioxide.
3. Difference between the summation of standard enthalpy of formation of product (step 2) and the summation of standard enthalpy of formation of reactants (step 1)

## Relation between Enthalpy, Entropy and Gibbs Free Energy

Enthalpy, Entropy and Gibbs free energy together are responsible for determining whether a thermodynamic system will undergo a spontaneous or a non-spontaneous reaction. Gibbs free energy is the maximum work done in a thermodynamic system when temperature and pressure are kept constant. Gibbs free energy is denoted by ‘G’, and as it is a type of energy, it is also expressed in Joules. Entropy is a physical property that is used to measure the amount of randomness in a system.

A Change in the Gibbs free energy is expressed as:

ΔG = ΔH – TΔS

Where ΔG= Change in Gibbs free energy

ΔH = Change in enthalpy

T= Temperature

ΔS= Change in entropy

ΔH (Change in Enthalpy) ΔS (Change in entropy) T ΔS ΔG (change in Gibbs free energy) The spontaneity of the reaction
+ - + + Non- spontaneous
- + - - spontaneous
- - + + or - Spontaneous at low temperature and non-spontaneous at high temperature
+ + - + or - Non-spontaneous at low temperature and spontaneous at high temperature.
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